A current i is carried by a long, straight wire. The magnetizing...

The magnetizing field intensity $H$ at a distance $r$ from a long straight wire carrying current $i$ is given by Ampere's law:

$\oint \vec{H} \cdot d\vec{l} = i_{free}$

$H = \dfrac{i}{2\pi r}$

The value of the magnetizing field $H$ depends only on the free current $i$ and the distance $r$. It is independent of the magnetic medium present. When a cylindrical iron rod is placed such that point $P$ is at its centre, the magnetic induction $B$ at $P$ increases many times because $B = \mu_r \mu_0 H$ and iron has a high relative permeability ($\mu_r \gg 1$). However, since the free current $i$ and the distance $r$ remain unchanged, the magnetizing field intensity $H$ remains almost constant.